Wei Lin

Learning causal relationships among a set of variables, as encoded by a directed acyclic graph, from observational data is complicated by the presence of unobserved confounders. Instrumental variables (IVs) are a popular remedy for this issue, but most existing methods either assume the validity of all IVs or postulate a specific form of relationship, such as a linear model, between the primary variables and the IVs. To overcome these limitations, we introduce a partially linear structural equation model for causal discovery and inference that accommodates potentially invalid IVs and allows for general dependence of the primary variables on the IVs. We establish identification under this semiparametric model by constructing surrogate valid IVs, and develop a finite-sample procedure for estimating the causal structures and effects. Theoretically, we show that our procedure consistently learns the causal structures, yields asymptotically normal estimates, and effectively controls the false discovery rate in edge recovery. Simulation studies demonstrate the superiority of our method over existing competitors, and an application to inferring gene regulatory networks in Alzheimer's disease illustrates its usefulness.

The particle filter (PF) and the ensemble Kalman filter (EnKF) are widely used for approximate inference in state-space models. From a Bayesian perspective, these algorithms represent the prior by an ensemble of particles and update it to the posterior with new observations over time. However, the PF often suffers from weight degeneracy in high-dimensional settings, whereas the EnKF relies on linear Gaussian assumptions that can introduce significant approximation errors. In this paper, we propose the Adversarial Transform Particle Filter (ATPF), a novel filtering framework that combines the strengths of the PF and the EnKF through adversarial learning. Specifically, importance sampling is used to ensure statistical consistency as in the PF, while adversarially learned transformations, such as neural networks, allow accurate posterior matching for nonlinear and non-Gaussian systems. In addition, we incorporate kernel methods to ease optimization and leverage regularization techniques based on optimal transport for better statistical properties and numerical stability. We provide theoretical guarantees, including generalization bounds for both the analysis and forecast steps of ATPF. Extensive experiments across various nonlinear and non-Gaussian scenarios demonstrate the effectiveness and practical advantages of our method.

1 IntroductionHigh-dimensional compositional data, which lie in a high-dimensional unit simplex, arise in a wide spectrum of contemporary applications. For example, in metagenomic studies, the comp...

High-dimensional compositional data are prevalent in many applications. The simplex constraint poses intrinsic challenges to inferring the conditional dependence relationships among the components forming a composition, as encoded by a large precision matrix. We introduce a precise specification of the compositional precision matrix and relate it to its basis counterpart, which is shown to be asymptotically identifiable under suitable sparsity assumptions. By exploiting this connection, we propose a composition adaptive regularized estimation (CARE) method for estimating the sparse basis precision matrix. We derive rates of convergence for the estimator and provide theoretical guarantees on support recovery and data-driven parameter tuning. Our theory reveals an intriguing trade-off between identification and estimation, thereby highlighting the blessing of dimensionality in compositional data analysis. In particular, in sufficiently high dimensions, the CARE estimator achieves minimax optimality and performs as well as if the basis were observed. We further discuss how our framework can be extended to handle data containing zeros, including sampling zeros and structural zeros. The advantages of CARE over existing methods are illustrated by simulation studies and an application to inferring microbial ecological networks in the human gut.

A New Nonsparse Learning Methodology for High-Dimensional Data Analysis Is Coming

The efforts of using data assimilation to improve PM_2.5 forecasts have been hindered by the limited number of species and incomplete vertical coverage in the observations. The common practice of initializing a chemical transport model (CTM) with assimilated initial conditions (ICs) may lead to model imbalances, which could confine the impacts of assimilated ICs within a day. To address this challenge, we introduce an Initial Error Transport Model (IETM) approach to improving PM_2.5 forecasts. The model describes the transport of initial errors by advection, diffusion, and decay processes, and calculates the impacts of assimilated ICs separately from the CTM. The CTM forecasts with unassimilated ICs are then corrected by the IETM output. We implement our method to improve PM_2.5 forecasts over central and eastern China. The reduced root-mean-square errors for 1- to 4-day forecasts during January 2018 are 51.2, 27.0, 16.4, and 9.4 μg m^-3, respectively, which are 3.2, 6.9, 8.6, and 10.4 times those by the CTM forecasts with assimilated ICs. More pronounced improvements are found for highly reactive PM_2.5 components. These and similar results for July 2017 suggest that our method can enhance and extend the impacts of the assimilated data without being affected by the imbalance issue.

Although air pollution is caused by emission of pollutants to the atmosphere,the observed pollution levels are confounded by meteorological conditions,which largely determine the dispersion of the pollutants.Hence, effective air-quality management requires the evaluation index and statistical measuresthat are immune to meteorological confounding and reflect changes in pollutant concentrations accurately and objectively.Motivated by the task of assessing changes in the underlying emission in a region near Beijing, we propose a spatial and temporal adjustment approach to remove meteorological confounding. The adjusted average pollutant concentration over space and time can capture changes in the underlying emission by controlling the meteorological variation. Estimation of the adjusted average is proposed together with theoretical and numerical analysis. We apply the approach to conducting air-quality assessments in the Beijing region, which reveals some intriguing patterns and trends that are useful for air-quality management.

Clustered multinomial data are prevalent in a variety of applications such as microbiome studies, where metagenomic sequencing data are summarized as multinomial counts for a large number of bacterial taxa per subject. Count normalization with ad hoc zero adjustment tends to result in poor estimates of abundances for taxa with zero or small counts. To account for heterogeneity and overdispersion in such data, we suggest using the logistic normal multinomial (LNM) model with an arbitrary correlation structure to simultaneously estimate the taxa compositions by borrowing information across subjects. We overcome the computational difficulties in high dimensions by developing a stochastic approximation EM algorithm with Hamiltonian Monte Carlo sampling for scalable parameter estimation in the LNM model. The ill-conditioning problem due to unstructured covariance is further mitigated by a covariance-regularized estimator with a condition number constraint. The advantages of the proposed methods are illustrated through simulations and an application to human gut microbiome data.

Many modern big data applications feature large scale in both numbers of responses and predictors. Better statistical efficiency and scientific insights can be enabled by understanding the large-scale response-predictor association network structures via layers of sparse latent factors ranked by importance. Yet sparsity and orthogonality have been two largely incompatible goals. To accommodate both features, in this paper, we suggest the method of sparse orthogonal factor regression (SOFAR) via the sparse singular value decomposition with orthogonality constrained optimization to learn the underlying association networks, with broad applications to both unsupervised and supervised learning tasks, such as biclustering with sparse singular value decomposition, sparse principal component analysis, sparse factor analysis, and spare vector autoregression analysis. Exploiting the framework of convexity-assisted nonconvex optimization, we derive nonasymptotic error bounds for the suggested procedure characterizing the theoretical advantages. The statistical guarantees are powered by an efficient SOFAR algorithm with convergence property. Both computational and theoretical advantages of our procedure are demonstrated with several simulations and real data examples.